Blow up in the Cauchy problem for a nonlinearly damped wave equation
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چکیده
In this paper we consider the Cauchy problem for the nonlinearly damped wave equation with nonlinear source utt −∆u + aut|ut|m−2 = bu|u|p−2, p > m. We prove that given any time T > 0, there exist always initial data with sufficiently negative initial energy, for which the solution blows up in time ≤ T. This result improves an earlier one by Todorova [11].
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تاریخ انتشار 2003